# The matrix of regressors for the Scheffe quadratic mixture model
# with 3 mixture components, each with levels {0, 0.25, 0.5, 0.75, 1}.
F.simplex(~x1 + x2 + x3 + I(x1*x2) + I(x1*x3) + I(x2*x3) - 1, 3, 5)
# The matrix of regressors for a "special cubic" model with 3 mixture
# components, each with levels {0, 0.2, 0.4, 0.6, 0.8, 1}.
F.simplex(~x1 + x2 + x3 + I(x1*x2) + I(x1*x3) + I(x2*x3) +
I(x1*x2*x3) - 1, 3, 6)
# Note that one must be careful when choosing a model for a mixture
# experiment: Let us compute the matrix of regressors of the simple
# linear mixture model with 4 mixture components, each with levels
# {0, 0.5, 1}.
F1 <- F.simplex(~x1 + x2 + x3 + x4, 4, 3)
# The model has only 4 parameters and as many as 10 design points,
# but there is no design that guarantees estimability of the
# parameters. This can be shown by evaluating:
det(od.infmat(F1, rep(1, 10)))
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